We study diffraction of Bessel vortex beams with topological charges of ±1 and ±2 and a wavelength of 130 µm on two-dimensional amplitude periodic gratings. Results of simulations and experiments at the Novosibirsk Free Electron Laser facility show that there appear periodic patterns in the planes corresponding to the classical main and fractional Talbot planes, but instead of self-images of the holes, there are observed periodic lattices of annular vortex microbeams with topological charges corresponding to the charge of the beam illuminating the grating. The ring diameters are the same for beams with different topological charges, but they are proportional to the grating period and inversely proportional to the diameter of the beam illuminating the grating.

In this paper, an analytical theory for the diffraction of a Bessel beam of arbitrary order J l (κr) on a 2D amplitude grating is presented. The diffraction pattern in the main and fractional Talbot planes under certain conditions is a lattice of annular microbeams, the diameters of which depend on the grating period, the illuminating beam diameter, the number of the Talbot plane, and the topological charge l. For the rings near the optical axis, the latter reproduces l of the illuminating beam. Experiments carried out on the Novosibirsk free electron laser at a wavelength λ = 141 µm using gratings with hole diameters of down to d ≈ 2λ, as well as, the numerical simulations, well support the theory. Since the Laguerre-Gaussian beams can be represented as a superposition of Bessel beams, results of this paper can be applied to the analysis of the Talbot effect with the Laguerre-Gaussian beams.

Transformation of a Bessel beam by a lens results in the formation of a “perfect” vortex beam (PVB) in the focal plane of the lens. The PVB has a single-ring cross-section and carries an orbital angular momentum (OAM) equal to the OAM of the “parent” beam. PVBs have numerous applications based on the assumption of their ideal ring-type structure. For instance, we proposed using terahertz PVBs to excite vortex surface plasmon polaritons propagating along cylindrical conductors and the creation of plasmon multiplex communication lines in the future (Comput. Opt. 2019, 43, 992). Recently, we demonstrated the formation of PVBs in the terahertz range using a Bessel beam produced using a spiral binary silicon axicon (Phys. Rev. A 2017, 96, 023846). It was shown that, in that case, the PVB was not annular, but was split into nested spiral segments, which was obviously a consequence of the method of Bessel beam generation. The search for methods of producing perfect beams with characteristics approaching theoretically possible ones is a topical task. Since for the terahertz range, there are no devices like spatial modulators of light in the visible range, the main method for controlling the mode composition of beams is the use of diffractive optical elements. In this work, we investigated the characteristics of perfect beams, the parent beams being quasi-Bessel beams created by three types of diffractive phase axicons made of high-resistivity silicon: binary, kinoform, and “holographic”. The amplitude-phase distributions of the field in real perfect beams were calculated numerically in the approximation of the scalar diffraction theory. An analytical expression was obtained for the case of the binary axicon. It was shown that a distribution closest to an ideal vortex was obtained using a holographic axicon. The resulting distributions were compared with experimental and theoretical distributions of the evanescent field of a plasmon near the gold–zinc sulfide–air surface at different thicknesses of the dielectric layer, and recommendations for experiments were given.